Question
1.1) \( -2 x+3=11 \) 1.2) \( 2-3(x+3)=2 x+3 \) 1.3) \( 5(x+2)=5 x+10 \) 1.4) \( 5(y-2)-2(y+1)=3(y-5) \)
Ask by Mckenzie Davies. in South Africa
Mar 09,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
1.1) \( x = -4 \)
1.2) \( x = -2 \)
1.3) All real numbers (\( x \in \mathbb{R} \))
1.4) No solution
Solution
1.1) Solve \( -2x + 3 = 11 \):
- Subtract \(3\) from both sides:
\[
-2x = 11 - 3 = 8
\]
- Divide by \(-2\):
\[
x = \frac{8}{-2} = -4
\]
---
1.2) Solve \( 2 - 3(x+3) = 2x + 3 \):
- Expand the left-hand side:
\[
2 - 3x - 9 = 2x + 3
\]
- Combine like terms:
\[
-3x - 7 = 2x + 3
\]
- Add \(3x\) to both sides:
\[
-7 = 5x + 3
\]
- Subtract \(3\) from both sides:
\[
-10 = 5x
\]
- Divide by \(5\):
\[
x = -2
\]
---
1.3) Solve \( 5(x+2) = 5x + 10 \):
- Expand the left-hand side:
\[
5x + 10 = 5x + 10
\]
Since both sides are identical, the equation is true for every \(x\):
\[
x \in \mathbb{R}
\]
---
1.4) Solve \( 5(y-2) - 2(y+1) = 3(y-5) \):
- Expand both sides:
\[
5y - 10 - 2y - 2 = 3y - 15
\]
- Combine like terms on the left:
\[
3y - 12 = 3y - 15
\]
- Subtract \(3y\) from both sides:
\[
-12 = -15
\]
Since \(-12 \neq -15\), the equation has no solution.
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Simplify this solution Mind Expander
Let’s make those equations fun and functional! First up, did you know that solving equations like these has roots tracing back to ancient civilizations? The Babylonians used an early form of algebra around 2000 BC, laying the groundwork for how we solve equations today. Imagine scribbling in cuneiform while figuring out your math problems! Now, here's a nifty tip: Always balance the equation! When you perform an operation on one side, do the exact same thing on the other side. A common mistake is to change only one side, which can lead to wrong answers—goodbye math mishaps! Remember, like a seesaw, both sides need to match for it to work!
